Question

Using only the 68-95-99.7 rule answer the following question. Let the variable Z be a z-score of a normal distribution. Calculate P(Z ≤ 3).   Draw a picture of the situation first. Shade the area that corresponds to the desired proportion being sought.

Please explain how you would use the 68-95-99.7 rule to solve this. If you can, how would you solve this using technology rather than the rule?

Answer 1

Solution :

Using Empirical rule,

P($\mu$ - 3$\sigma$< X < $\mu$ + 3$\sigma$) = 99.7%

P(Z $\leq$ 3) = 0.9985